Infrared Behavior of Dipolar Bose Systems at Low Temperatures

Abstract

We rigorously discuss the infrared behavior of the uniform three-dimensional dipolar Bose systems. In particular, it is shown that low-temperature physics of the system is controlled by two parameters, namely isothermal compressibility and intensity of the dipole–dipole interaction. By using a hydrodynamic approach, we calculate the spectrum and damping of low-lying excitations and analyze the infrared behavior of the one-particle Green’s function. The low-temperature corrections to the anisotropic superfluid density as well as condensate depletion are found. Additionally, we derive equations of the two-fluid hydrodynamics for dipolar Bose systems and calculate velocities of first and second sound.

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Acknowledgments

We thank Prof. I. Vakarchuk and Dr. A. Rovenchak for stimulating discussions. This work was partly supported by Project FF-30F (No. 0116U001539) from the Ministry of Education and Science of Ukraine.

Appendix

In this section, we present the explicit expressions for the imaginary parts of the exact second-order vertices in the low-length limit. The leading-order contribution is determined by all diagrams with only two vertices, namely \(D_{\varphi \varphi \rho }(K,Q|P)\) and \(D_{\rho \rho \rho }(K,Q,P)\). Feynman diagrams contributing to \(\mathfrak {R}\Pi _{\varphi \rho }(\omega ,\mathbf{k})\) and \(\mathfrak {I}\Pi _{\rho \rho }(\omega ,\mathbf{k})\) are given in Figs. 2 and 3, respectively. In the same manner, the low-energy behavior of \(\mathfrak {I}\Pi _{\varphi \varphi }(\omega ,\mathbf{k})\) can be easily obtained from Fig. 1. For convenience terms contributing to the Beliaev damping